The goal of optical waveform measurement is to measure the variations of a waveform in time. Optical waveforms may be characterized in the time domain by an intensity and a phase. Optical waveforms also may be characterized in the frequency domain by taking the Fourier transform of the time domain representation. In the frequency domain, an optical waveform may be characterized by a spectral intensity (or spectrum) and a spectral phase. The derivative of the spectral phase with respect to frequency may be computed to obtain the “group delay,” which represents the delay in the arrival time of a particular slice of the spectrum at a frequency at a particular location. If the group delay is constant, all frequencies arrive at the same time, and the pulse is as short as possible.
Many different techniques for measuring optical waveforms have been proposed. If the waveform variations are sufficiently slow, a waveform may be measured directly using electronic equipment, such as oscilloscopes, photodiodes, and streak cameras. For faster waveform variations, intensity autocorrelation waveform measuring techniques may be used to determine some aspects of an optical waveform. Such techniques involve crossing a waveform and a delayed replica of the waveform in a nonlinear medium, such as a second-harmonic-generation crystal or a two-photon absorber, and detecting the output optical energy as a function of delay. Time-frequency domain optical waveform measurement techniques also have been proposed. In these techniques, the intensity variations over time are measured for different spectral slices of an optical waveform. More complex waveform measurement methods, such as frequency-resolved optical gating techniques, also have been proposed. In these techniques, the spectrogram of an optical waveform pulse is measured. The gating occurs in time, rather than frequency, followed by measurement of the spectrum of each time slice. Typically, the optical waveform is gated with itself. The resulting spectrogram is a spectrum of the autocorrelation.